Question

4. The production technology of a firm is described by a production function Q=L+2K where L represents the number of labor hours and K the number of machine hours used in the production process. The hourly wage and rental rates are given by w and r. Calculate the total cost function for the firm when both L and K are variable inputs. (Hint: A graph may be helpful.)

Show and explain all calculations. Draw graphs whenever necessary. Provide economic reasoning.

Answer 1

Answer 2

4) Production faction is given by:- Q = Lt 2x MP - Q. - 1. AL Ja 2 : and MPK ak Now, suppose input puces for L and k one w and 8 respectively. L MPK . This when wy2 =) MPL z MPK > MPL =) MPK Hace, fim will use only k input and optical outfont will be found by substititg 2=0 in the production fiction. Hice, Q = 0 +2K :) - K Now, cost fuction C= WL trk C-ot rQ 2 -) 2 e = 8Q 2 When, WLD then MPL MPK and firm will use only I and optial input will be tond by substitiling k=0 in the production faction. tice, Q=lto =) L=Q Hice, cost function: c= whitrk- WQ =) C- WQ CS Scanned with CamScanner

the cost bicton & c=rQ for wyn 2 WhN tor WQ CS Scanned with CamScanner